Abstract:
The last few decades have seen a broadening of the
philosophy of mathematics, beyond narrowly logical, foundational, and
metaphysical issues, towards more general questions concerning mathematical
methodology and mathematical practice. In this talk, I will contribute to
this broadening, specifically to what has been called a "new
epistemology" for mathematics. By considering the case of Richard
Dedekind and his contributions to algebraic number theory in the nineteenth
century, I will attempt to bring into sharper focus, and to argue for the
relevance of, the notions of "style of reasoning" and
"mathematical understanding".